Simplify the following expression and state the condition under which the simplification is valid: $n = \dfrac{y^2 + y - 56}{y^2 + 8y}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{y^2 + y - 56}{y^2 + 8y} = \dfrac{(y - 7)(y + 8)}{(y)(y + 8)} $ Notice that the term $(y + 8)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(y + 8)$ gives: $n = \dfrac{y - 7}{y}$ Since we divided by $(y + 8)$, $y \neq -8$. $n = \dfrac{y - 7}{y}; \space y \neq -8$